We report the synthesis of three out-of-plane chemically ordered quaternary transition metal borides (o-MAB phases) of the chemical formula M4CrSiB2 (M = Mo, W, Nb). The addition of these phases to the recently discovered o-MAB phase Ti4MoSiB2 shows that this is indeed a new family of chemically ordered atomic laminates. Furthermore, our results expand the attainable chemistry of the traditional M5SiB2 MAB phases to also include Cr. The crystal structure and chemical ordering of the produced materials were investigated using high-resolution scanning transmission electron microscopy and X-ray diffraction by applying Rietveld refinement. Additionally, calculations based on density functional theory were performed to investigate the Cr preference for occupying the minority 4c Wyckoff site, thereby inducing chemical order.